A local multivariate Lagrange interpolation method for constructing shape functions

摘要

In this paper, the conventional global univariate Lagrange interpolation method is transformed into a local multivariate interpolation method. The method has the following attractive features: it can be used to interpolate irregularly distributed data points; it does not need to solve local problems; if used for constructing shape functions, the obtained shape functions satisfy the Kronecker delta condition and they have the reproducing properties. The performance of the local multivariate Lagrange interpolation method was examined by applying it to function approximation.